Story Problem: a box is to be constructed by cutting 1 inch squares...?

Question

from the corners of the rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 112in^3 ?

Answer 1

The finished box is 1" high, so the area is 112 square inches. Given width W, we have:

A = 112 = (W-2)(2W-2) = 3W^2 - 6W + 4

Solving for W gets you 9, and 2W would be 18. To check:

7 x 16 = 112

Answer 2

volume of cube=x^3
surface area is 6x^2
if y=volume then x=cube root of y and
surface area is 6*(cube root y)^2

the area of sheet above would be 2z^2

the area of the sheet should match surface area of cube
so
2z^2=6*(cube root y)^2
or
z^2=3*(cube root y)^2
substitute y
z^2=3*(cube root 112)^2
z=square root (3*(cuberoot(112)^2) )